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If f x = e - 1 x 2   ∀ x ≠ 0 and f 0 = 0 , then f ′ 0 is

Options

  1. Anot defined
  2. B1
  3. C0
  4. D2

Correct answer

C. 0

Step-by-step solution

R f ' 0 = lim h → 0 e - 1 0 + h 2 − 0 h = lim h → 0 1 h e − 1 h 2 = lim h → 0 ⁡ 1 h e 1 h 2 = lim h → 0 − 1 h 2 e 1 h 2 ⋅ − 2 h 3 = lim h → 0 ⁡ h 2 e 1 h 2 = 0 ∞ = 0 L f ' 0 = lim h → 0 e − 1 0 − h 2 − 0 − h = lim h → 0 − 1 h e − 1 h 2 = lim h → 0 ⁡ - 1 h e 1 h 2 = lim h → 0 ⁡ 1 h 2 e 1 h 2 - 2 h 3 = lim h → 0 ⁡ h - 2 e 1 h 2 = 0 ∞ = 0 Hence, f ' 0 =

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